Strong Ground Motion and Concept of Response Spectrum February 2012 Sudhir K Jain, IIT Gandhinagar
Sudhir K. Jain
February 2012
1
EQ Ground Motions
Low Amplitude Vibrations
Long distance events Usually displacements Earth Scientists
Amplitude
Teleseismic Earthquake Recording
0
Sudhir K. Jain
200
Surface Waves
S
PP
P
400
600
800
February 2012
1000
1200 Time (s)
Slide 2
EQ Ground Motions…
Strong Ground Motions
Near-field ground motions Usually accelerations Engineers 0.3 PGA=0.32g
Accn. (g)
0.2 0.1 0 -0.1 -0.2 -0.3 0
Sudhir K. Jain
10
20
30
40 50 Time (seconds)
February 2012
60
70
80
Slide 3
Peak Ground Parameters
Acceleration (PGA) Velocity (PGV) Displacement (PGD)
Sudhir K. Jain
February 2012
Slide 4
Maximum Recorded Motion
Sudhir K. Jain
February 2012
(Martinez-Pereira, 1999) Slide 5
Characteristics…
Parameters…
Duration of Significant Shaking Frequency Content 1985 Mexico Earthquake (SCT 1A; N90E)
0.5g
1940 Imperial Valley Earthquake (El Centro; S00E)
1971 San Fernando Earthquake (Pacoima Dam; N76W)
0
10
20
30
40
50
60 Time (sec)
1991 Uttarkashi Earthquake (Uttarkashi, N75E)
Sudhir K. Jain
February 2012
Slide 6
Characteristics
Influence of
Magnitude of EQ Source mechanism
Fault
Type of faulting
Fault
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Distance from source Soil/rock medium along travel path Local soil site, geology, topology, etc.,. February 2012
Attenuation with Distance Slide 7
Accelerogram
During ground shaking, one can measure ground acceleration versus time (accelerogram) using an accelerograph
Accelerograph is the instrument Accelerogram is the record obtained from it
Sudhir K. Jain
Accelerogram is the variation of ground acceleration with time (also called time history of ground motion)
February 2012
Slide 8
Typical Accelerograph
This is a typical analog instrument. These days, digital instruments are becoming popular (photo from Earthquakes by Bolt) Sudhir K. Jain
February 2012
Slide 9
Typical Accelerograms
From Dynamics of Structures by A K Chopra, Prentice Hall
Time, sec
Sudhir K. Jain
February 2012
Slide 10
Response Spectrum (contd…)
If the ground moves as per the given accelerogram, what is the maximum response of a single degree of freedom (SDOF) system (of given natural period and damping)? Response may mean any quantity of interest, e.g., deformation, acceleration
T=2 sec, Damping =2% a(t)/g
Ground motion time history Sudhir K. Jain
Time, sec February 2012
Slide 11
Response Spectrum (contd…)
Using a computer, one can calculate the response of SDOF system with time (time history of response) Can pick maximum response of this SDOF system (of given T and damping) from this response time history
Sudhir K. Jain
See next slide
February 2012
Slide 12
Response Spectrum (contd…) Maximum response = 7.47 in.
d(t)
Time, sec
Time History of Deformation (relative displacement of mass with respect to base) response
T=2 sec, Damping =2%
a(t)/g Time, sec
Ground motion time history
Sudhir K. Jain
February 2012
Slide 13
Response Spectrum (contd…)
Repeat this exercise for different values of natural period. For design, we usually need only the maximum response. Hence, for future use, plot maximum response versus natural period (for a given value of damping). Such a plot of maximum response versus natural period for a given accelerogram is called response spectrum.
Sudhir K. Jain
February 2012
Slide 14
Response Spectrum (contd…) Displacement Response Spectrum for the above time history
ag(t)/g
Time, sec
T=0.5 sec =2% d(t)/g
dmax
T=1.0 sec =2% d(t)/g
T=2.0 sec =2% d(t)/g
Time, sec Sudhir K. Jain
Figure After Chopra, 2001 February 2012
T, sec Slide 15
Response Spectrum (contd…)
Response Spectrum is useful to obtain maximum response of any SDOF system for that accelerogram and for that value of damping. See example on next slide
Sudhir K. Jain
February 2012
Slide 16
Natural Period T=1 sec Damping =5% of critical
3m
From Response Spectrum: Spectral Acceleration (for T=1sec) = 0.48 g
Max. Base Shear = Mass x Spectral Accln. =(10,000kg) x (0.48x9.81m/sec2) = 47,000 N = 47 kN Max. Base Moment
=(47kN) x (3m) = 141 kN-m
Sudhir K. Jain
Time (sec) Ground Acceleration Time History
Maximum Acceleration, g
Mass = 10,000kg
Acceleration, g
Example
Undamped Natural Period T (sec) Acceleration Response Spectrum for the above accelerogram for 5% damping (Fig. from Seed and Idriss, 1982) February 2012
Slide 17
Response Spectrum (contd…)
May repeat the entire process for different values of damping
Velocity response spectra for N-S component of 1940 El Centro record (damping values of 0, 2, 5 and 10%) Fig From Housner, 1970 Sudhir K. Jain
Maximum Velocity, in/sec
Natural Period T (sec)
February 2012
Slide 18
Response Spectrum (contd…)
Unless otherwise mentioned, response spectrum is based on a linear elastic system
Sudhir K. Jain
February 2012
Slide 19
Response Spectrum (contd…)
By response we may mean any response quantity of interest to us, for example:
Absolute acceleration of the mass
Relative velocity of the mass with respect to base
Termed as Velocity Response Spectrum
Relative displacement of the mass with respect to base
Termed as Acceleration Response Spectrum
Termed as Displacement Response Spectrum
Word Spectra is used to denote plural of Spectrum.
Sudhir K. Jain
February 2012
Slide 20
Response Spectrum (contd…)
Since SDOF system responds maximum to the waves of frequency near its own natural frequency,
Response spectrum is also a very good way to characterize the strong ground motion from engineering view point.
Sudhir K. Jain
For instance, relative strength of low frequency versus high frequency waves
See example on next slide
February 2012
Slide 21
Velocity, ft/sec
Example: Velocity spectra from two accelerograms
Natural Period T (sec) Note that the two response spectra above show very different frequency content. Ground motion B has more energy at low periods. An expert may be able to make out from these spectra that B is recorded at a short distance (say 15km) from a small earthquake, while A is recorded from a large earthquake at a large distance (say 100km) (Fig. edited from Housner, 1970) Sudhir K. Jain
February 2012
Slide 22
Response Spectrum (contd…)
Response spectrum is a very powerful tool. Uses of response spectrum:
Sudhir K. Jain
To obtain maximum response of a SDOF system (to the original accelerogram using which response spectrum was obtained) To obtain maximum response in a particular mode of vibration of a multi degree of freedom (MDOF) system It tells about the characteristics of the ground motion (accelerogram)
February 2012
Slide 23
Response Spectrum (contd…)
Different terms used in IS:1893
Design Acceleration Spectrum (clause 3.5) Response Spectrum (clause 3.27) Acceleration Response Spectrum (used in cl. 3.30) Design Spectrum (title of cl. 6.4) Structural Response Factor Average response acceleration coefficient (see terminology of Sa/g on p. 11) Title of Fig. 2: Response Spectra for ….
It is better if the code uses the term consistently.
Sudhir K. Jain
February 2012
Slide 24
Smooth Response Spectrum
Real spectrum has somewhat irregular shape with local peaks and valleys For design purpose, local peaks and valleys should be ignored
Since natural period cannot be calculated with that much accuracy.
Hence, smooth response spectrum used for design purposes For developing design spectra, one also needs to consider other issues
Sudhir K. Jain
We will discuss this later. February 2012
Slide 25
Smooth Response Spectrum (contd…)
Period (sec)
Acceleration Spectra
Period (sec)
Velocity Spectra
Period (sec)
Displacement Spectra
Shown here are typical smooth spectra used in design for different values of damping (Fig. from Housner, 1970)
Sudhir K. Jain
February 2012
Slide 26
Ground Acceleration (contd...)
Note the term Peak Ground Acceleration (PGA) is max acceleration of ground.
Because of deformation in the structure, the motion of its base and the superstructure will be different Max acceleration experienced by mass of the structure will be different from the PGA (except if the structure is rigid)
Sudhir K. Jain
February 2012
Slide 27
Ground Acceleration
ZPA stands for Zero Period Acceleration.
Sudhir K. Jain
Implies max acceleration experienced by a structure having zero natural period (T=0).
February 2012
Slide 28
Zero Period Acceleration
An infinitely rigid structure
Has zero natural period (T=0) Does not deform:
No relative motion between its mass and its base Mass has same acceleration as of the ground
Hence, ZPA is same as Peak Ground Acceleration
Sudhir K. Jain
For very low values of period, acceleration spectrum tends to be equal to PGA. We should be able to read the value of PGA from an acceleration spectrum. February 2012
Slide 29
Peak Ground Acceleration (contd…)
Average shape of acceleration response spectrum for 5% damping (Fig. on next slide)
There can be a stray peak in the ground motion; i.e., unusually large peak.
Ordinate at 0.1 to 0.3 sec ~ 2.5 times the PGA
Such a peak does not affect most of the response spectrum and needs to be ignored.
Effective Peak Ground Acceleration (EPGA) defined as 0.40 times the spectral acceleration in 0.1 to 0.3 sec range (cl. 3.11)
Sudhir K. Jain
There are also other definitions of EPGA, but we will not concern ourselves with those. February 2012
Slide 30
Typical shape of acceleration spectrum 1.80 1.60
Spectral Acceleration (g)
1.40 1.20 1.00 0.80
0.60 0.40
PGA = 0.6g
0.20 0.00 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Period (sec)
•Typical shape of acceleration response spectrum •Spectral acceleration at zero period (T=0) gives PGA •Value at 0.1-0.3 sec is ~ 2.5 times PGA value (for 5% damping) Sudhir K. Jain
February 2012
Slide 31
What is Design Spectrum
Seismic Design Force can be specified in terms of Response Spectrum:
Sudhir K. Jain
Termed as Design Spectrum
February 2012
Slide 32
Response Spectrum versus Design Spectrum
Spectral Acceleration, g
Consider the Acceleration Response Spectrum Notice the region of red circle marked: a slight change in natural period can lead to large variation in maximum acceleration
Undamped Natural Period T (sec) Sudhir K. Jain
February 2012
Slide 33
Response Spectrum versus Design Spectrum (contd…)
Natural period of a civil engineering structure cannot be calculated precisely Design specification should not very sensitive to a small change in natural period. Hence, design spectrum is a smooth or average shape without local peaks and valleys you see in the response spectrum
Sudhir K. Jain
February 2012
Slide 34
Design Spectrum
Since some damage is expected and accepted in the structure during strong shaking, design spectrum is developed considering the overstrength, redundancy, and ductility in the structure. The site may be prone to shaking from large but distant earthquakes as well as from medium but nearby earthquakes: design spectrum may account for these as well.
Sudhir K. Jain
See Fig. next slide.
February 2012
Slide 35
Spectral Acceleration, g
Design Spectrum (contd…)
Natural vibration period Tn, sec Fig. from Dynamics of Structures by Chopra, 2001 Sudhir K. Jain
February 2012
Slide 36
Design Spectrum (contd…)
Design Spectrum is a design specification It must take into account any issues that have bearing on seismic safety.
Sudhir K. Jain
February 2012
Slide 37
Design Spectrum (contd…)
Design Spectrum must be accompanied by:
Load factors or permissible stresses that must be used
Damping to be used in design
Depending on modeling assumptions, one can get different values of natural period.
Type of detailing for ductility
Sudhir K. Jain
Variation in the value of damping used will affect the design force.
Method of calculation of natural period
Different choice of load factors will give different seismic safety to the structure
Design force can be lowered if structure has higher ductility. February 2012
Slide 38
Soil Effect
Recorded earthquake motions show that response spectrum shape differs for different type of soil profile at the site
Fig. from Geotechnical Earthquake Engineering, by Kramer, 1996
Period (sec) Sudhir K. Jain
February 2012
Slide 39
Soil Effect (contd…)
This variation in ground motion characteristic for different sites is now accounted for through different shapes of response spectrum for three types of sites. Spectral Acceleration Coefficient (Sa /g)
Fig. from IS:1893-2002
Period(s) Sudhir K. Jain
February 2012
Slide 40
Shape of Design Spectrum
The three curves in Fig. 2 have been drawn based on general trends of average response spectra shapes. In recent years, the US codes (UBC, NEHRP and IBC) have provided more sophistication wherein the shape of design spectrum varies from area to area depending on the ground motion characteristics expected.
Sudhir K. Jain
February 2012
Slide 41
Design Spectrum for Stiff Structures
For very stiff structures (T < 0.1sec), ductility is not helpful in reducing the design force. As a stiff structure gets damaged during the Design spectrum assumes peak extends to T=0 shaking, its period Actual shape of response spectrum elongates (may be used for higher modes only)
i.e., during the same ground shaking, a very stiff structure may ride up the ascending part of the graph.
Codes tend to disallow the reduction in force in the period range of T < 0.1sec
Spectral acceleration
T(seconds) Concept sometimes used by the codes for response spectrum in low period range.
Sudhir K. Jain
February 2012
Slide 42
